Yeh-Multiscale Finite Element Method for Simulation of Darcy Velocity of Water Flow in Porous Media
A porous medium, multi-scale technology, applied in the field of hydraulics, can solve the problems such as the inability to guarantee the continuity of velocity and flow, and the lack of solving the Darcy infiltration velocity, etc., to achieve the effect of high precision, obvious efficiency advantages, and high computing efficiency.
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Embodiment 1
[0070] Embodiment 1: two-dimensional oscillating medium model
[0071] The research area is a square unit: Ω=[0,1m]×[0,1m], the water flow equation is:
[0072]
[0073] The permeability coefficient is:
[0074]
[0075] where P 1 =1.965,P 2 = 1.99, the source-sink term W and the constant head boundary are determined by the analytical solution H=xy(1-x)(1-y).
[0076] The model is solved using MSFEM-Y, Method-Yeh, Method-Zhang and Method-Yeh-F. In order to ensure the same number of coarse grid nodes, MSFEM-Y, Method-Yeh and Method-Zhang all divided each side of the study area into the same 30 parts (N=30), a total of 1800 (2NN) triangular units ( figure 1 ). MSFEM-Y divides each unit into 25 fine grid units ( figure 2 ). In order to ensure that the number of cells is the same as the number of fine grid cells in MSFEM-Y, Method-Yeh-F divided each side of the study area into 150 parts (N=150), with a total of 45,000 fine grid cells.
[0077] Coarse-scale Darcy per...
Embodiment 2
[0085] Example 2: Two-dimensional gradient medium unsteady flow model
[0086] The research area is a square unit: Ω=[0,1m]×[0,1m], the water flow equation is:
[0087]
[0088] Permeability coefficient K(x,y)=(1+x)(1+y)m / d. The water storage coefficient is 0.1 / m, the aquifer thickness is 1 m, the time step is 1 day, and the total time is 5 days. The source-sink term W and the fixed head boundary are solved analytically: H=xy(1-x)(1-y)e -t Sure.
[0089] The model is solved using MSFEM-Y, Method-Yeh, Method-Zhang and Method-Yeh-F. The subdivision is the same as in the first embodiment above, that is, MSFEM-Y, Method-Yeh and Method-Zhang subdivide the study area into 1800 units, MSFEM-Y subdivides each coarse grid into 25 fine units, and Method- Yeh-F divided the study area into 45000 units.
[0090] Coarse-scale Darcy percolation velocity
[0091]Same as the above-mentioned Example 1, MSFEM-Y and Method-Yeh-F obtained more accurate head values than other methods, MS...
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